The following is just a supplement to the OP's own research and the excellent answers already provided.
What is at issue is pre-head complementation vs. pre-head modification
Technically speaking, the OP is asking whether in a construction of the type X scold, X can function as a complement of the head noun scold, as opposed to acting as a mere modifier of it.
To explain that, here are two cases where X is not a pre-head complement, but just a pre-head modifier:
[a] this might be Louise Hay or any of the other smiling New Age scolds who
tell their unhappy followers that they chose their AIDS or abusive parents (source);
[b] Germany's balancing act between euro scold and bailout enabler (source);
We should contrast these with
 Mike is a deficit scold.
First of all, there is a semantic difference.
In [a], being New Age is indirectly predicated of Louise Hay (and others); the sentence implies that Louise Hay is a New Age 'person'. Similarly, in [b], euro is indirectly predicated of Germany; the sentence implies that Germany is a 'euro' entity, i.e. a member of the Eurozone.
In contrast, in , deficit is not predicated of Mike. Rather, deficit is wholly 'subordinate' to scold; Mike is related to defict only through scold.
The general technical statement is that complements express semantic arguments of the head noun (CGEL, p. 441). In all three cases [a], [b], and , the head noun is scold (or scolds). But only in  does the nominal before scold express a semantic property of scold, namely, the subject concerning which the scolding occurs. In , the scolding occurs in the area of deficits. But in [a], it is not the case that the scolding occurs in the area of New Age. Neither the New Age part in [a] nor the euro part in [b] is especially connected to being a scold.
Another way to see the difference between [a] and [b] on one hand, and  on the other, is to note that  has a close paraphrase involving post-head complements with a forced choice of preposition; the part about 'forced choice' is called licensing and is 'the most basic criterion for complement status of post-head dependents' (CGEL, p. 440). In particular, we can paraphrase  as
[1'] Mike is a scold of deficits.
Here we have little choice as to which preposition to use. Note that there are no corresponding paraphrases of either [a] or [b].
Further examples of nominals that can serve as pre-head complements of scold
The Oxford Dictionary, already referenced by the OP, also gives the following example of usage:
 it may not be as bad as some lifestyle scolds make it out to be (original source here)
The context (see the link) makes it clear that we are talking about scolds of (certain kinds of) lifestyle; so indeed here lifestyle functions as a pre-head complement of scolds.
Here are some other examples:
 the support of Obama-era nutrition scolds (source);
don't be a nutrition scold on Halloween (source);
 But today's education scolds have no such excuse. (source);
 immigration scolds seem to be excessively afraid (source);
 an iPhone and Android app that functions as a mobile spending scold (source);
All of these are instances of scold(s) having a pre-head complement. A nutrition scold is a scold of certain nutrition practices; an education scold is a scold of certain kinds of educational practices (or of the state of education); and so on.